tl;dr: Looks like SpaceX could save fuel/weight by landing more aggressively. Could they? Will they?

I've tried to do a bit of calculating based on the wonderful video analysis that Hrissan provided of the OG2 landing. I was trying to figure out just how efficient the landing was in terms of propellant used to decelerate the stage vs cancelling gravity, and then throw some hypothetical aggressive landing scenarios and see how those would look comparatively. Anyway, heres some preliminary results followed by some questions I have for the community.

Assumptions and observations: 145m/s terminal velocity (Hrissan stated "about" 150, but my eyeballs say a little less, plus it fits the deceleration estimates/times better)Initial deceleration regime of 4m/s/s for 10s Final deceleration regime of 7.5m/s/s for 14s These two regimes are about 20% apart in impulse, which lines up well with an assumption of 100%-62% throttle range and 10% throttle buffer on both ends.Assuming no major sources of aerodynamic drag during the landing burns.Assuming constant thrust AND deceleration for each regime. (which we all know can't be true, hoping it wont throw off the results too much)Assuming constant engine ISP through different throttle settings such that a given % drop of thrust will produce the same % drop in Mdot.I used 282s ISP and 273kg/s Mdot.

From this I came up with an actual landing that used 5415kg of propellant to produce 380m/s of total impulse while slowing the stage by 145m/s for a total efficiency of 38.1% (62% of the thrusting merely cancelled out gravity)

I created a few different hypothetical scenarios some of which may be unrealistic or even fully impossible.

MB1 (Make Believe 1):1 landing engine, 1 thrust regime (90% throttle)Burn would last 19.3 seconds @ 7.5m/s/s deceleration, using 4748kg of fuel while providing 334m/s of total impulse for total efficiency of 43.4% and a fuel savings of 667kg from the baseline.

MB2:3 landing engines 1 thrust regime (72% throttle)Burn would last 4.6 seconds @ 31.6m/s/s deceleration, using 2718kg of fuel while providing 190m/s of total impulse for total efficiency of 76.3% and a fuel savings of 2697kg (!) from the baseline.

MB3: 3 landing engines 2 thrust regimes and 2 engine shutdown @ stage velocity of 40m/s (72% throttle on all 3 initially with final landing on 90% single engine)First burn would last 3.3 seconds @ 31.6m/s/s using 1962kg of fuel while providing 138 m/s of total impulse.Second Burn would last 5.3 seconds @ 7.5m/s/s using 1304kg of fuel while providing 92 m/s of total impulse.All together 3266kg of Fuel, 230m/s of impulse, efficiency of 63% and a fuel savings of 2149kg from the baseline.

MB2 is obviously the most crazy. stable landing control with three thrusting engines and a final T/W of over 4.2 is far from assured. Of course one could imagine a scenario with three engines firing at 90% till landing, but that one seemed too crazy for me to even bother modeling.

MB3 is still very aggressive even with a final T/W no worse than already demonstrated -- Still only 3.3 seconds (including startup and shutdown transients) for the three engine burn and only 5.3 seconds to iron out a final landing solution.

MB1 is very tame merely doing away with the initial low throttle period, but still managing to save over 600kg of fuel.

So, first off can anyone point out any obvious math errors? (i know "total impulse" for breaking + Gravity losses is probably the wrong terminology) Beyond the feasibility of my scenarios, I would like to know if I didn't even calc the fuel use to within an order of magnitude.

But more interestingly, how useful is a fuel savings of about 2000kg? or even just 600kg? Is there any reason to expect that SpaceX will attempt to land more aggressively and really push the limits?

I don't want to say that I was disappointed by the landing, but it wasn't exactly as "brown pants" of a maneuver as I was expecting. But maybe my perception betrays just how difficult of landing it already was?

Anyway, after doing all these calcs I figured that with how much use I get out this forum, that I should try to give back and hope someone else finds this interesting as well. It is now way too late for me to still be awake please forgive typos.

I think the entry burn is far more critical to save fuel. That's a three engine burn already.But a higher acceleration landing is desirable as it saves fuel but also reduces the stage exposure to winds.I don't think it will ever mean using two engines though.Running the center engine at 100% of original thrust (around 85% of upgraded thrust) is a heck of a lot of thrust. The stage is very light. It also leaves the question of any variability in restart times. If you push too hard, even a fraction of a second = not enough time to land.This will likely be a gradual process where SpaceX will slowly push the envelope until they fail (or some metric is achieved).

SpaceX will likely push this on ASDS landings. Where the most they have to loose is the stage itself (ASDS cheaper than incoming stage), and in missions where fuel is more likely to be short.

1) savings on 1st stage do not translate directly on payload increase2) increases risk considerably3) decision between expendable or reusable will come from the payload mass and target orbit and probably the decision will not be different if there is a bit more upmass capability.

I wonder what's really preventing them from deploying the landing legs earlier. That would save fuel in theory, but maybe it's a question of aerodynamic stability even assuming the legs would stay rigid, but maybe there is a risk that the legs would bend and oscillate.

I wonder what's really preventing them from deploying the landing legs earlier. That would save fuel in theory, but maybe it's a question of aerodynamic stability even assuming the legs would stay rigid, but maybe there is a risk that the legs would bend and oscillate.

If the deploy mechanism would be changed to allow this they could do a partial deploy first. Make it look like an arrowhead. It would provide drag and keep the legs away from the flames. It should cause less stability issues too.

I wonder what's really preventing them from deploying the landing legs earlier. That would save fuel in theory, but maybe it's a question of aerodynamic stability even assuming the legs would stay rigid, but maybe there is a risk that the legs would bend and oscillate.

I think the legs could burn with rocket exhaust if exposed too soon.

Yes, we saw how badly the metal Grashopper legs got smoked. SpaceX obviously wants to reuse these F9 composite legs which will be more easily damaged by heat than the metal GH legs, and the obvious way to preserve them is to minimize time on the barbecue grill.

I think a likely required part of the landing burn is correction of targeting errors from using just the grid fins. Unless the grid fins are pinpoint accurate, you want to start the burn early so the rocket has time to adjust for the final targeted location. Even then, upper-layer winds might push the stage off-target and the grid fins might not be able to compensate as much as the engine can. This might be a limiting factor in starting the burn later, however many engines are used.

I wonder what's really preventing them from deploying the landing legs earlier. That would save fuel in theory, but maybe it's a question of aerodynamic stability even assuming the legs would stay rigid, but maybe there is a risk that the legs would bend and oscillate.

I thought we understood the legs required deceleration force to deploy and thus couldn't deploy until the landing burn was in progress. Elon mentioned a redesign to allow the legs to act as airbrakes, have we heard anything about that since this 11/2014 tweet?

I think a likely required part of the landing burn is correction of targeting errors from using just the grid fins. Unless the grid fins are pinpoint accurate, you want to start the burn early so the rocket has time to adjust for the final targeted location. Even then, upper-layer winds might push the stage off-target and the grid fins might not be able to compensate as much as the engine can. This might be a limiting factor in starting the burn later, however many engines are used.

That's an unintuitive aspect of landing.The faster the vertical speed, the less winds will affect you (less time exposed to them).The sensors and computers on the stage detect wind effects instantly (1/10th of a second).The faster the vertical speed, the more control authority the grid fins have.

Finally you're assuming sideways control margins are tight. That might be right or very wrong.And cold gas thrusters add more control authority.

The fact SpaceX allows for 50mph winds for land landings suggest there are plenty of margins.

If the deploy mechanism would be changed to allow this they could do a partial deploy first. Make it look like an arrowhead. It would provide drag and keep the legs away from the flames. It should cause less stability issues too.

How would that partially deployed leg position effect the air flow in/around the grid fins?Would it cancel out your proposed stability enhancement?

Yes, we saw how badly the metal Grashopper legs got smoked. SpaceX obviously wants to reuse these F9 composite legs which will be more easily damaged by heat than the metal GH legs, and the obvious way to preserve them is to minimize time on the barbecue grill.

I recall that some of those later Grasshopper tests had the metal legs covered with a black material that the earlier flights did not. I always assumed it was SpaceX engineers covering the legs with some/all of the sorts of materials and/or coatings they were planning to use in the deployable legs design on F9 v1.1. I believe there was some discussion of this in other threads.

In other words, I suspect that a good bit of that extended smoking we observed was materials testing.

Now, back to the original idea of this thread by PreferToLurk: what about using different thrust and fuel usage regimes for saving propellant on hoverslam landings?

Logged

Re arguments from authority on NSF: "no one is exempt from error, and errors of authority are usually the worst kind. Taking your word for things without question is no different than a bracket design not being tested because the designer was an old hand.""You would actually save yourself time and effort if you were to use evidence and logic to make your points instead of wrapping yourself in the royal mantle of authority. The approach only works on sheep, not inquisitive, intelligent people."

I think a likely required part of the landing burn is correction of targeting errors from using just the grid fins. Unless the grid fins are pinpoint accurate, you want to start the burn early so the rocket has time to adjust for the final targeted location. Even then, upper-layer winds might push the stage off-target and the grid fins might not be able to compensate as much as the engine can. This might be a limiting factor in starting the burn later, however many engines are used.

That's an unintuitive aspect of landing.The faster the vertical speed, the less winds will affect you (less time exposed to them).

I'm talking about upper-layer winds, following the entry interface burn, and before the current powered landing envelope. This is the terminal velocity of the stage, so velocity is constant in this regime. It is true that the grid fins have more control authority at a higher speed, but we don't know that they are capable of a pinpoint landing without any engine burn. In other words, I am asserting the engine burn is not just to bring vertical velocity to zero, it is also to target the final landing point. I think this would be difficult to argue against. I'm further arguing that it is likely that the burn starts higher up, to allow the engine to target the pad with terminal guidance that the other systems are unlikely to be able to provide. This seems reasonable to me, but is clearly not proven.

Quote

Finally you're assuming sideways control margins are tight. That might be right or very wrong.

I don't think they have to be "tight" to prevent a last-second burn from being practical.

Quote

And cold gas thrusters add more control authority.

Cold gas thrusters are irrelevant for this purpose, they aren't very powerful and are on the wrong end of the stage to provide any real lateral displacement that late in the game.

Quote

The fact SpaceX allows for 50mph winds for land landings suggest there are plenty of margins.

With the engine burn, starting where it does, yes.

Finally, one purpose of the final burn appears to be a "divert" from an offshore-based trajectory to one that targets the pad. This divert did seem to happen in the successful landing. You'd probably have to eliminate the divert maneuver before considering reducing the final burn by any significant amount of time.

(As an aside, I have no issue with the hypothesis that SpaceX is being conservative where they are starting the engine burn, and that they might be able to reduce it over time. I think it is unlikely we will ever see a true "hoverslam" though).

But more interestingly, how useful is a fuel savings of about 2000kg? or even just 600kg? Is there any reason to expect that SpaceX will attempt to land more aggressively and really push the limits?

Here's a back-of-the-envelope calculation of how much this helps. I assume a GTO mission since all LEO missions so far have big margins anyway.

If you are super aggressive, you might save 2500 kg of fuel. Each engine uses 270 kg/sec, so that's 1 more second you can burn all 9 engines on ascent. Since you are accelerating at roughly 5 Gs at cutoff, that's 50 m/s more you might get from the first stage. So for the same payload mass, you could get 50 m/s more final delta-v. Compared to the 300 m/s differences between different GTO orbits, that's mildly helpful but not game-changing.

Alternatively, you could get a bigger payload to the original orbit. For GTO, the second stage needs about 8210 m/s ( https://forum.nasaspaceflight.com/index.php?topic=34077.msg1463298#msg1463298 ), so if it starts at 121 t, it masses 10,897 kg at cutoff. If it only needs 8160 m/s, then it masses 11,057 kg at cutoff, so the payload goes up by 160 kg. (These mass number have way too many significant digits, but the difference should be pretty close to the real value.) This only makes a difference for those few payloads right on the very edge of F9 performance, and even there the difference is not big.

If the fuel saved is only 600 kg, the improvements will be about 4x smaller. In either case, it's hard to see making a big change in landing strategy. A more aggressive throttle schedule with the current number engines? Perhaps. A three-engine landing burn to a screeching halt? Probably not worth the risk.

On the third hand, suppose you had an engine failure or some other under-performance on the way up. You make up for it by burning more fuel to fight more gravity losses. After achieving the correct velocity for the start of the second stage, you don't have enough fuel for a "conventional" landing. Now might be the right time to try a super-aggressive landing sequence - shorter than normal re-entry burn, followed by a minimal-hover maximum-slam landing. But it's hard to imagine SpaceX devoting the engineering resource needed to attempt a landing for such an unlikely case, plus you'd probably need extra inspections/refurbishment after a novel landing sequence even if it succeeded. So overall the screeching halt landings seem unlikely.

16Km is a LOT, but the stage will be compensating for that all the way through the descent, and I assume winds aloft will be uploaded prior to launch and the stage will be pre positioned to drift through that.

Weather forecasts and weather balloons pre launch are excellent at characterizing aloft winds.I also think those can be input into the descent profile.

It is true that the grid fins have more control authority at a higher speed, but we don't know that they are capable of a pinpoint landing without any engine burn. In other words, I am asserting the engine burn is not just to bring vertical velocity to zero, it is also to target the final landing point. I think this would be difficult to argue against.

Actually, it's extremely easy to argue against this. Smart bombs routinely achieve meter-level accuracy using only fins, and have for decades. It's well proven technology.

"One bit of advice: it is important to view knowledge as sort of a semantic tree -- make sure you understand the fundamental principles, ie the trunk and big branches, before you get into the leaves/details or there is nothing for them to hang on to." - Elon Musk"There are lies, damned lies, and launch schedules." - Larry J

It is true that the grid fins have more control authority at a higher speed, but we don't know that they are capable of a pinpoint landing without any engine burn. In other words, I am asserting the engine burn is not just to bring vertical velocity to zero, it is also to target the final landing point. I think this would be difficult to argue against.

Actually, it's extremely easy to argue against this. Smart bombs routinely achieve meter-level accuracy using only fins, and have for decades. It's well proven technology.

It is true that the grid fins have more control authority at a higher speed, but we don't know that they are capable of a pinpoint landing without any engine burn. In other words, I am asserting the engine burn is not just to bring vertical velocity to zero, it is also to target the final landing point. I think this would be difficult to argue against.

Actually, it's extremely easy to argue against this. Smart bombs routinely achieve meter-level accuracy using only fins, and have for decades. It's well proven technology.

Smart bombs have far more control authority and glide capability than a F9R stage.The state of the art in smart bomb is the SDB, which have been demonstrated to glide for tens of miles with high subsonic drop.In the cast of SDB, you have actual crude wings.Even a 500lb JDAM can glide much better than a F9R stage.

But as long as the stage can receive pre launch winds aloft programming, it can seek an estimated aim point at end of entry burn that lateral inertia + winds aloft will significantly reduce grid fin efforts in lateral navigation.

This is a well known technique in aircrafts in general. Easy peasy for the SpaceX software guys to program (compared to the other nightmares they have to handle in the whole RTLS/ASDS thing).

The altitudes where winds are the strongest (above 25k ft) are exactly where terminal speed is still significant (but subsonic), hence grid fins will have maximum effect.